There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Use an Excel spreadsheet to explore long multiplication.

Use an interactive Excel spreadsheet to investigate factors and multiples.

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to explore number in this exciting game!

Use Excel to investigate the effect of translations around a number grid.

Use Excel to explore multiplication of fractions.

An Excel spreadsheet with an investigation.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Here is a chance to play a fractions version of the classic Countdown Game.

Have you seen this way of doing multiplication ?

A metal puzzle which led to some mathematical questions.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Match the cards of the same value.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

Discover a handy way to describe reorderings and solve our anagram in the process.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

An environment that enables you to investigate tessellations of regular polygons

How good are you at finding the formula for a number pattern ?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

Practise your skills of proportional reasoning with this interactive haemocytometer.

Cellular is an animation that helps you make geometric sequences composed of square cells.

Can you beat the computer in the challenging strategy game?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

To avoid losing think of another very well known game where the patterns of play are similar.

A collection of our favourite pictorial problems, one for each day of Advent.

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.